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On moving averages and asymptotic equipartition of information

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Abstract

We prove a moving average version of the Shannon–McMillan–Breiman theorem.

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References

  1. M.A. Akcoglu, A. del Junco, Convergence of averages of point transformations. Proc. Am. Math. Soc. 49, 265–266 (1975)

    MATH  Google Scholar 

  2. A. Bellow, R. Jones, J. Rosenblatt, Convergence of moving averages. Ergod. Theory Dyn. Syst. 10(1), 43–62 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Bellow, V. Losert, The weighted ergodic theorem and individual ergodic theorem along subsequences. Trans. Amer. Math. Soc. 288, 307–345 (1985)

  4. L. Breiman, The individual ergodic theorem of information theory. Ann. Math. Stat. 28(3), 809–811 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  5. A.P. Calderón, Ergodic theory and translation-invariant operators. Proc. Nat. Acad. Sci. USA. 59, 349–353 (1968)

    Article  MATH  Google Scholar 

  6. I.P. Cornfeld, S.V. Fomin, Ya G. Sinai, Ergodic Theory, Grundlehren der Mathematischen Wissenschaften, vol. 245 (Springer, New York, 1982). x+486 pp.

    Google Scholar 

  7. T. Cover, J. Thomas, Elements of Information Theory, 2nd edn. (Wiley, Newyork, 2006)

    MATH  Google Scholar 

  8. J.L. Doob, Stochastic Processes (Wiley, New York, 1953)

    MATH  Google Scholar 

  9. H. Kamarul-Haili, R. Nair, On moving averages and continued fractions Unif. Distrib. Theory 6(1), 65–78 (2011)

    MathSciNet  Google Scholar 

  10. H. Kamarul-Haili, R. Nair, Optimal continued fractions and the moving average ergodic theorem. Period. Math. Hung. 66(1), 95–103 (2013)

    Article  MathSciNet  Google Scholar 

  11. H. Kamarul-Haili, R. Nair, The nearest integer continued fraction and the moving average ergodic theorem. Unif. Distrib. Theory 8(1), 73–87 (2013)

    MathSciNet  Google Scholar 

  12. B. McMillan, The basic theorems of Information. Ann. Math. Stat. 24, 196–219 (1953)

    Article  MathSciNet  Google Scholar 

  13. A. Nagel, E.M. Stein, On certain maximal functions and approach regions. Adv. Math. 54(1), 83–106 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Schwartz, Polynomially moving ergodic averages. Proc. Am. Math. Soc. 103(1), 252–254 (1988)

    Article  MATH  Google Scholar 

  15. C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J. 27, pp.379–423,623–656 (1948)

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX, UK

    Radhakrishnan Nair

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  1. Radhakrishnan Nair
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Correspondence to Radhakrishnan Nair.

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Nair, R. On moving averages and asymptotic equipartition of information. Period Math Hung 71, 59–63 (2015). https://doi.org/10.1007/s10998-014-0080-x

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  • DOI: https://doi.org/10.1007/s10998-014-0080-x

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